X2540

INSIMILICENTER(NINE-POINT CIRCLE, SPIEKER RADICAL CIRCLE)

X2540 is the insimilicenter(nine-point circle, Spieker radical circle).
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 5, 10 }: Central Line L(5, 10) { 2, 2537 }: Central Line L(2, 2537) { 4, 2536 }: Central Line L(4, 2536) { 11, 2534 }: Central Line L(11, 2534) { 12, 2535 }: Central Line L(12, 2535) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_2 = CENTROID (0.5374, 0.2000) X_2537 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.4272, -0.1877) X_4 = ORTHOCENTER (0.6122, 0.3958) X_2536 = INSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.5089, 0.1377) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_2534 = INSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE) (0.5580, 0.2201) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_2535 = EXSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE) (0.5998, 0.2610) X_2540 = INSIMILICENTER(NINE-POINT CIRCLE, SPIEKER RADICAL CIRCLE) (0.5461, 0.2305) A B C X5 X10 X2 X2537 X4 X2536 X11 X2534 X12 X2535 X2540 (a, b, c) = (5, 6, 7) | AB = 1

X2540 (INSIMILICENTER(NINE-POINT CIRCLE, SPIEKER RADICAL CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[(b + c)r + ad(\cos A + 2 \cos B \cos C)]\), where \(d = (r^{2} + s^{2})^{1/2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.430369985003\)
▸ Incident Central Lines5 lines

{2, 2537}, {4, 2536}, {5, 10}, {11, 2534}, {12, 2535}

Notes

See X2534.